Collective modes in multiband superconductors

We theoretically investigate collective modes in a minimal model of a multiband superconductor. Specifically, we consider a two-band model which results from an additional sublattice degree of freedom and includes all symmetry-allowed spin-orbit coupling and inter-sublattice hopping terms. Starting from a uniform BCS ground state, we derive a Gaussian effective action for the condensate, including fluctuations into competing odd-parity channels. We find that the spin-orbit coupling is essential for the existence of these fluctuations, and evaluate the possibility for the experimental detection of the associated collective modes.